(Solved): Q1 - Sum to n terms For each series find the term required and the sum of the terms. 2+4+8+16+4+ ...

Q1 - Sum to $$\mathrm{n}$$ terms For each series find the term required and the sum of the terms. $$\begin{array}{lll}2+4+8+16+\dots & 6\text{ th term }=& S_8=\\ 4+12+36+108+\dots & \text{ 8th term }=& S_{10}=\end{array}$$ Write each series using sigma notation and find the sum of the terms. Give your answers to 3 d.p. where appropriate. $$\begin{array}{r}4+20+100+500+\dots ={?}_{n=1}^9\times \\ 0.8+3.6+16.2+\dots ={?}_{n=1}^6\times \end{array}$$ ?2 - Sum to infinity Find the sum to infinity of these series. $$5+2.5+1.25+\dots S_{?=1}^{?}=$$ The first 4 terms of a geometric series are $$6+1.2+0.24+0.048$$ Write down an expression for the $$n$$th term. [2] Write down a simplified expression for the sum to $$n$$ terms. Find the sum to infinity. [2]